The following is an incomplete table for the... | WAEC SSCE - General Mathematics - 1990 (Essay)

Question 1 Report

The following is an incomplete table for the relation \(y = 2x^{2} - 5x + 1\)

x	-3	-2	-1	0	1	2	3	4	5
y			8	1		-1			26

(a) Copy and complete the table.

(b) Using a scale of 2cm to 1 unit on the x- axis and 2cm to 10 units on the y- axis, draw the graph of the relation \(y = 2x^{2} - 5x + 1\) for \(-3 \leq x \leq 5\).

(d) Estimate from your graphs, correct to one decimal place : (i) the least value of y and the value of x for which it occurs ; (ii) the solution of the equation \(2x^{2} - 5x + 1 = x + 6\).

Answer

Answer Details

(a) Completing the table for \(y = 2x^{2} - 5x + 1\)

Substitute each x-value, for example \(x=-3:\; 2(9)-5(-3)+1 = 18+15+1 = 34\).

x	-3	-2	-1	0	1	2	3	4	5
y	34	19	8	1	-2	-1	4	13	26

(b) The graph

Plot the nine points with 2 cm to 1 unit on the x-axis and 2 cm to 10 units on the y-axis, and join them with a smooth U-shaped parabola.

(c) The line \(y = x + 6\)

Use two points: at \(x=-3,\;y=3\) and at \(x=5,\;y=11\). Draw the straight line through \((-3,3)\) and \((5,11)\).

(d)(i) Least value of y

The lowest point of the parabola occurs at the vertex, \(x = \dfrac{5}{2\times 2} = 1.25\). Then

\(y = 2(1.25)^{2} - 5(1.25) + 1 = 3.125 - 6.25 + 1 = -2.125\).

From the graph, the least value of y is \(\approx -2.1\), occurring at \(x \approx 1.3\).

(d)(ii) Solution of \(2x^{2} - 5x + 1 = x + 6\)

The solutions are the x-coordinates where the curve meets the line. Algebraically:

\(2x^{2} - 5x + 1 = x + 6 \Rightarrow 2x^{2} - 6x - 5 = 0\).

\(x = \dfrac{6 \pm \sqrt{36+40}}{4} = \dfrac{6 \pm \sqrt{76}}{4}\), giving \(x \approx 3.7\) and \(x \approx -0.7\).

Read lesson note on Algebraic Expressions (WAEC)

Read lesson note on Coordinate Geometry (JAMB)

Read lesson note on Quadratic Equations (WAEC)

Algebraic Expressions

Coordinate Geometry

Quadratic Equations

View Answer

The following is an incomplete table for the relation \(y = 2x^{2} - 5x + 1\) x -3 -2 -1 0 1 2 3 4 5 y 8 1 -1 26 (a) Copy and complete the table. (b) Using ...

Download The App On Google Playstore

The following is an incomplete table for the relation \(y = 2x^{2} - 5x + 1\) x -3 -2 -1 0 1 2 3 4 5 y 8 1 -1 26 (a) Copy and complete the table. (b) Using ...

Related Questions

Download The App On Google Playstore